Job Scheduling Problem

Duration: 7 min

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Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Mensuration and Geometry, Age Problems, Arithmetic, Statistics, Probability, Profit and Loss, Simple Interest and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, Powers and Exponents (Surds and Indices), Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy
  3. Paper-1 & 2 | Data Interpretation: Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Analogy, Ranking, Order and Sequence, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Data Arrangement, Logical Sequence Of Words, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: Selection Decision Table (Decision Making)
  7. Paper-1 | General Science: Physics, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: State Wise GK, GK- Current Affairs
  9. Paper-2 | Fundamentals of Computer: Basics of COA, Number System, Floating Point Rep, Number Representation
  10. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits
  11. Paper-2 | Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Linux OS, Distributed Systems
  12. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  13. Paper-2 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  14. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  15. Paper 2 | Oops, C++, Java: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  16. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  17. Paper 2 | Emerging Trends and AI: Emerging Tech Trends, Artificial Intelligence
  18. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Advanced Algorithms
  19. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security, Ethical Hacking
  20. Paper-2 I Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  21. Paper-2 | Computer Organization and Architecture: Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations
  22. Paper-2 | Web Development: JavaScript-Basics, HTML Basics, CSS, XML
  23. Pedagogy: Child Development, Concept of Pedagogy, Psychology, Theories, Inclusive Education, Experiential Pedagogy, Curriculum Framework & Reforms, National Education Policy (NEP) 2020
  24. Live Sessions: RSSB Live Sessions
  25. RSSB Paper 1 - Full Mock Tests:
  26. RSSB Paper 2 - Full Mock Tests:
  27. SCI Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video lecture introduces the Job Scheduling Problem, a classic optimization problem in computer science. The instructor begins by defining the problem parameters on a slide: a single CPU, non-primitive scheduling, and n-jobs where each job has an arrival time of 0, a burst time of 1, a deadline Di, and a profit Pi. The objective is to select a subset of jobs that can be completed within their deadlines to maximize total profit. A visual chart titled '10X10 Job Shop Scheduling Problem' is displayed to illustrate an unconstrained schedule. The lecture then transitions to a specific numerical example from a GATE 2005 exam question involving 9 tasks (T1 to T9). The instructor demonstrates a greedy algorithm approach, drawing a timeline and filling slots with tasks based on their profits and deadlines to determine the optimal schedule and identify which tasks must be left out.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor presents the problem definition on a slide titled 'Job scheduling problem'. He highlights key constraints: 'single CPU with Non-Primitive Scheduling and n-jobs'. He specifies that 'arrival time is 0, burst time of each job requirement is 1'. The goal is to 'Select a Subset of 'n' jobs, such that, the jobs in the subset can be completed with in the deadline and generate Max profit.' A chart labeled '10X10 Job Shop Scheduling Problem' shows colored bars representing an 'Unconstrained Schedule'. The instructor underlines 'Non-Primitive Scheduling' and circles 'deadline Di'. He writes 'J1 -> S' on the screen, indicating the mapping of a job to a time slot. The slide also mentions 'Knowledge Gate Educator' and 'Sanchit Jain Sir' in the bottom left corner.

  2. 2:00 – 5:00 02:00-05:00

    The slide changes to a specific problem statement: 'Q. We are given 9 tasks T1, T2... T9.' A table lists tasks, profits, and deadlines. For example, T3 has profit 30 and deadline 5. T1 has profit 15 and deadline 7. The question asks, 'Are all tasks completed in the schedule that gives maximum profit? (Gate-2005) (2 Marks)'. Four options are provided: (A) All tasks are completed, (B) T1 and T6 are left out, (C) T1 and T8 are left out, (D) T4 and T6 are left out. The instructor draws a timeline with 9 boxes labeled 1 through 9. He begins solving by writing 'T3' into slot 3, as it has the highest profit (30) and a deadline of 5. He then writes 'T7' into slot 2 (profit 23, deadline 2).

  3. 5:00 – 6:50 05:00-06:50

    The instructor continues filling the timeline to construct the optimal schedule. He writes 'T9' (profit 25, deadline 3) into slot 1. He places 'T2' (profit 20, deadline 2) into slot 2, but then adjusts. Looking at the final board state, the slots are filled as: Slot 1 with T2, Slot 2 with T7, Slot 3 with T9, Slot 4 with T5, Slot 5 with T3, Slot 6 with T1, and Slot 7 with T8. This arrangement satisfies all deadlines. The tasks T4 and T6 are not placed in any slot. The instructor concludes that T4 and T6 are the tasks left out, corresponding to option (D). The board shows the final schedule clearly.

The lecture effectively bridges theoretical problem definition with practical application. It starts by establishing the constraints of the Job Scheduling Problem, emphasizing the trade-off between deadlines and profits. The instructor then applies a greedy strategy to a concrete example, visually demonstrating how to map tasks to time slots. By sorting tasks by profit and placing them in the latest possible slot before their deadline, he derives the optimal subset of jobs. The final board state clearly shows which tasks are feasible and which are excluded, reinforcing the algorithmic approach to solving scheduling problems.

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